Solve 4(-3)+x^2=1

$$4 ( - 3 ) + x ^ { 2 } = 1$$

Solve for x

$$x=\sqrt{13}\approx 3.605551275$$

$$x=-\sqrt{13}\approx -3.605551275$$

Steps by Finding Square Root

Multiply 4 and -3 to get -12.

$$-12+x^{2}=1$$

Add 12 to both sides.

$$x^{2}=1+12$$

Add 1 and 12 to get 13.

$$x^{2}=13$$

Take the square root of both sides of the equation.

$$x=\sqrt{13} x=-\sqrt{13}$$

Steps Using the Quadratic Formula

Multiply 4 and -3 to get -12.

$$-12+x^{2}=1$$

Subtract 1 from both sides.

$$-12+x^{2}-1=0$$

Subtract 1 from -12 to get -13.

$$-13+x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$x^{2}-13=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -13 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-13\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-13\right)}}{2}$$

Multiply -4 times -13.

$$x=\frac{0±\sqrt{52}}{2}$$

Take the square root of 52.

$$x=\frac{0±2\sqrt{13}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{13}}{2} when ± is plus.

$$x=\sqrt{13}$$

Now solve the equation x=\frac{0±2\sqrt{13}}{2} when ± is minus.

$$x=-\sqrt{13}$$

The equation is now solved.

$$x=\sqrt{13} x=-\sqrt{13}$$